Quantum Hall $p-n$ Junction Dartboards Using Graphene Annuli

TL;DR

This paper demonstrates the use of graphene $p-n$ junction dartboards with multiple terminals to measure fractional quantum Hall resistances, supported by simulations and scalable fabrication techniques.

Contribution

It introduces quantum Hall resistance dartboards with Corbino geometries for fractional resistance measurements and validates their design through experiments and simulations.

Findings

Measured fractional quantum Hall resistances at the $ u=2$ plateau.

Simulations show potential parameter space for device output.

Ultraviolet lithography enables scalable device fabrication.

Abstract

The use of multiple current terminals on millimeter-scale graphene $p-n$ junction devices fabricated with Corbino geometries, or quantum Hall resistance dartboards, have enabled the measurement of several fractional multiples of the quantized Hall resistance at the $\nu=2$ plateau ($R_H\approx 12906 {\Omega}$). Experimentally obtained values agreed with corresponding numerical simulations performed with the LTspice circuit simulator. More complicated designs of the quantum Hall resistance dartboard were simulated to establish the potential parameter space within which these Corbino-type devices could output resistance. Most importantly, these measurements support simpler processes of ultraviolet lithography as a more efficient means of scaling up graphene-based device sizes while maintaining sufficiently narrow junctions.